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Fibonacci Calculator

Enter your low price and high price below, and press 'Calculate' to generate Fibonacci retracements across key ratios.

What is a Fibonacci calculator?

The Fibonacci calculator generates four levels (23.8%, 38.2%, 50% and 61.8%) between a low price and a high price. For reasons that remain unclear, these levels appear to play an important in the financial markets just as they do in nature, and have been used by traders to identify support and resistance levels at which a currency or a stock price is likely to change course. It is common practice to set take-profit and stop-loss orders either at or near these levels.

Where do these levels come from?

These levels, also known as retracement ratios, are closely related to the Fibonacci sequence, uncovered by the Italian mathematician Leonardo of Pisa in the 13th century. The Fibonacci sequence is an infinite series of numbers created by summing the previous two numbers, as follows:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89...

Remarkably, these numbers are also related to one another through what is known as the golden ratio or phi, a number approximately equal to 1.6180339887.... in the sense that every number is approximately equal to the previous number multiplied by the golden ratio.

55 * 1.618 = 88.99

Likewise, dividing one number by its successor in the sequence returns the inverse of the golden ratio, one of the key retracement ratios:

55 / 89 = 0.618 which is equal to 1 / 1.618 = 0.618 or 61.8%

Moving down the sequence by one number yield yet another retracement ratio:

34 / 89 = 0.382 or 38.2%

For reasons that remain unclear, these ratios appear to play an important in the financial markets just as they do in nature, and have been used by traders to identify price points where an asset's price is likely to change course.

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